Question:

Find $\displaystyle \frac{f(x+h)-f(x)}{h} $ where h is not equal to zero and $\displaystyle f(x)=\sqrt{x} $.

Attempt:

$\displaystyle = \frac{\sqrt{x+h}-\sqrt{x}}{h} $

I have to rationalize the numrator

$\displaystyle = \frac{(\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}}{h(\sqrt{x+h}+\sqrt{ x}} $

Now how to simplify?

Thank you